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Basic Math

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Basic Math

Significant Figures and Scientific Notation

How long is the snake ?

1m

1m

0.1m = 10 cm

1m

0.01m = 1 cm

How long is the snake ?

0.3 m

1m

0.27 m

1m

0.1m = 10 cm

0.270 m

1m

0.01m = 1 cm

- Rule 1- which digits are significant: The digits in a measurement that are considered significant are
- all of those digits that represent marked calibrations on the measuring device plus one additional
- digit to represent the estimated digit (tenths of the smallest calibration).

- The sum or difference of measurements may have no more decimal places than the least number of places in any measurement.

Ans: 29.8 m

- When multiplying or dividing, the number of significant figures retained may not exceed the least number of digits in either the of the factors.

0.304 cm x 73.84168 cm =

22.4 cm2

Note: only display three (3) significant figures because 0.304 only has threesignificant figures.

- What is the number:
602,214,150,000,000,000,000,000

- Avogadro’s number.
- How do we usually see this?
6.0221415x1023

or

6.0221415e+23

- Why do we display it in this form?

- Gravitational Constant (very small)
6.67 × 10-11 C = 6.67e-11

- Coulomb’s Constant (very big):
8.99 × 109 = 8.99e+9

- Charge on an electron (very small)
1.60217646 × 10-19 = 1.602e-19

- Practice with gravitational constant:
6.67e-11

- Type “6.67”
- Type “2nd-,”
- Type Negative
(NOT minus) 11

6.67

6.67E

6.67E-11

- Force between two large bodies:

239 N

- Force between two charges:

Unit Conversions

Importance of Units and how to convert between Units

- Convert 3,600,000 to scientific notation
- 3.6E6 or 3.6 x 106

- Convert 0.00435 to scientific notation
- 4.35e-3 or 4.35 x 10-3

- Convert 8.99E9 (or 8.99 x 109)to standard notation
- 8,990,000,000

- Convert 6.67E-5 (or 6.67 x 10-5) to standard notation
- 0.0000667

- Someone wants to sell you a car for 100.
- Is this a good deal?

- You cannot determine if this is a good deal unless you know the units.
- $1k units ($100,000 for a car? – too high)
- $1 units ($100 – probably pretty good)
- $10 units ($1,000 – depends on car)
- $0.01 (i.e. 1¢) – ($1.00 for car – great deal!)

- There are seven (7) base units in the SI system. All other units are derived from these.
- How many can you name?

acceleration

force

frequency

volume

velocity

velocity

- What if someone wanted to sell you their car for 5,000 £ (British pounds). Is this a good deal?
- We need to convert units
- We can convert units because
- it is always okay to multiply something by 1.
- Any number divided by itself (or its equivalent) is always equal to 1
- As long as numerator and denominator are equivalent, the number is equal to 1.
- $1.5782 is equal to 1 £. How much is 5,000 £ ?
- $1 is equal to 0.6336 £. Does this change the conversion?

OR

- Always okay to multiply by 1
- We are NEVER changing the original quantity (just the way we look at it)
- Which is more $1 or 100¢ ?

- Ensure the undesirable units ‘cancel out’
- One instance should be in numerator (top)
- Other instance should be in denominator (bottom)

- The distance to San Antonio is 197 miles. How many km is this? (1 km = 0.62 miles)
- 318 km

- A sack of cement is 50 kg. How heavy is this in lbs (1 kg = 2.2 lbs)
- 110 lbs

- The speed limit is 65 mph. How fast is this in km/hr (1 mph = 1.60934 km/hr)
- 105 km/hr

- How many seconds in a day?
- 86,400

- How many seconds in 3:45:15?
- 13,515

- A dropped object achieves a speed of 39.8 m/s. How fast is that in mph? (there are 1.60934 km in 1 mile).

- VesnaVulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6miles, 551 yards. What is the distance in meters? (there are 1.60934 km in 1 mile, and 1inch = 2.54 cm).

- Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (km/h) and (b) meters per second (m/s)?

Additional Practice available from worksheets

Functions

Using functions and using basic algebra to manipulate functions

1. Read the problem carefully.

2. Identify the quantity to be found.

3. Identify the quantities that are given in the problem.

4. Identify the equation that contains these quantities.

5. Solve the equation for the unknown.

6. Substitute the value given in the problem, along with their proper units, into the equation and solve it.

7. Check to see if the answer will be correct in the correct units. (dimensional analysis)

8. Check your answer to see if it reasonable.

- Simply plugging in the numbers represented by the variables
- And calculating the desired result
- Must put the equation in the “proper” form before you can do this
- Rearrange the formula so that the desired variable is all by itself on the left:
- i.e. Y= {some messy equation}

- Use appropriate formula to calculate “average velocity” if an object moves a distance of 923 miles in 14 hours. (you can leave the answer in mph)

- Use the appropriate formula to calculate net force that is applied if a mass of 3,900 kg (a Hummer) is accelerated 2.43 m/s2 .
- 9501 kg·m/s2

- Use the appropriate formula to calculate the acceleration required to move an object with an initial velocity (vi) of 0 m/s, a final velocity (vf) of 26.8 m/s, over a displacement (Δd) of 147.4 m.
- 2.43 m/s2

- Sometimes the desired variable is in the wrong place, so we must “solve” for the desired variable (get it all by itself and on top)
- On simple formulas we can Cross multiply
- This works because we can always multiply each side of function by same number

- Use formula charts
- Show that there is “one” function
- Create two (2) additional ones

- If you are planning on a scientific/math oriented career (including business medical fields, computers) – need to master basic algebra skills (including formula manipulations)

- Can create for any ‘proportional’ equation

- Awkward and does not really work for added variables or complex equations

- Solve the following equation for displacement (Δd). Then solve for time (Δt).

- Moving a value
- always can add to one side, if we add the same to the other side
- Always can subtract from one side if we subtract same from the other side

- Solve for x:

- Using the averaged velocity function, solve the following:
- The average velocity of the speed of light is 3e8 m/s. It takes 8 minutes (8*60 seconds) for light to reach the earth from the sun. How far is the sun?
- 144,000,000 km

- If Michael Phelps swims 1.667 m/s for 2 minutes (120 seconds), how far has he swam?
- 200 m

- The average velocity of the speed of light is 3e8 m/s. It takes 8 minutes (8*60 seconds) for light to reach the earth from the sun. How far is the sun?

- Solve for vi =

- Solved for vi=
- Or: